In Section 4 we study simplicial principal bundles in \({K}/B\)  or more generally
in a category \({C}\)  admitting finite limits. Our treatment here is heavily influenced
by Duskin's memoir [1]}. We explain how the
universal simplicial principal bundle for a group \(G\)  in \(s{C}\)  gives rise,
via the Artin-Mazur total simplicial object functor \(T\colon ss{C}\rightarrow s{C}\) ,
to the classical universal bundle \(WG\rightarrow \overline{W}G\) . We show (Lemma REF ) how
this perspective on the classical \(\overline{W}\)  construction equips \(WG\)  with a
canonical structure as a simplicial group, an observation that seems
to be missing from the literature. We also give a new treatment
of the classifying map for a principal twisted cartesian product and show how the
bundle gerbes of Murray [2]} have a natural interpretation as
principal twisted cartesian products.
